The present invention relates generally to determining the signal-to-noise-ratio in a received signal transmission and more particularly to a system and method of use for a computer-implemented signal-to-noise-ratio estimation process for aiding in signal demodulation and message recovery or as an indication of recovered message fidelity.
All communication systems are susceptible to interfering signals normally referred to as noise. The interfering signals may have harmful effects on the performance of any communication system. These effects depend on the specific system being used, on the nature of the noise and the way it interacts with the signal without noise, and on the relative intensity of the noise compared to that signal. The intensity of the noise compared to that of the signal is usually measured by the signal-to-noise-ratio (SNR), which is the ratio of the power of the signal to the power of the noise. Signal receivers, in attempting to demodulate a signal and recover its contents, need to be able to accurately estimate the SNR.
The present invention is a computer-implemented signal-to-noise ratio (SNR) estimator that produces estimates of the true channel SNR and tracks changes in the channel noise power over time. It can be used by many receivers as an aid to demodulation and message recovery or as an indication of recovered message fidelity. It operates on a collection of received data probability density functions (PDFs), either contained in closed form equations or stored in lookup tables. It allows for the estimation of both the instantaneous and average signal-to-noise ratio (SNR) values. The invention can be generally used as a noise power estimator or SNR estimator for dynamic threshold level determination in a receiver with nonstationary (time-varying) noise, or a receiver whose received signal comprises data with unequal a priori transmit probabilities, such as encoded binary antipodal messages whose codes are structured to contain more zeros than ones or vice versa. SNR determination is required in some communications systems to estimate recovered messaged fidelity, for example to provide circular error probability figures on location calculations in global positioning satellite (GPPS) receivers and for hand off algorithms in cellular mobile communications receivers. The average SNR estimator can be used with many types of communication systems including spread spectrum systems, encrypted secure communications systems, chaotic communication systems, and LPD systems utilizing receiver-feedback transmit power level control.
The present invention comprises method in a computer system for determining a signal-to-noise ratio (SNR) in a signal comprising, for each iterate value of the signal: calculating an instantaneous maximum likelihood SNR; calculating a current average SNR value as a running weighted average of the instantaneous maximum likelihood SNR; and using the current average SNR value as feedback to the instantaneous maximum likelihood SNR to determine if a local instantaneous maximum likelihood value close to the current average SNR value exists, and if a local instantaneous maximum likelihood value close to the current average SNR exists, saving the local instantaneous maximum likelihood value as the SNR for the value of the signal. If a local instantaneous maximum likelihood value close to the current average SNR does not exist, a global maximum value is saved as the SNR for the value of the signal. If a local maximum instantaneous likelihood value does not exist, the global maximum value is the maximum likelihood SNR value closest to the current average SNR estimate. The instantaneous maximum likelihood SNR may be determined using a lookup-table and may comprise the SNR having the largest probability density function value for the iterate value of the signal. The instantaneous maximum likelihood SNR may also be derived using closed form equations. The closed form equations comprise: modeling a transmit probability density function (PDF) as a DC level plus a summation of weighted Gaussian functions; modeling the channel noise PDF as a Gaussian function; convolving the transmit PDF function model with the noise PDF model to determine the received PDF model as a function of the instantaneous SNR; using the received PDF model for the received value; and determining an instantaneous maximum probability SNR for the received value using an iterative root approximation optimization technique. The iterative root approximation technique may use Newton-Raphson equations or modified Newton-Raphson equations. The method using modified Newton-Raphson equations comprises: finding a maxima of the probability function of SNR; limiting a maximum correction per step to detect the maxima of the probability function of SNR; and multiplying a computed step size by at least two factors to prevent missing a peak, wherein the peak indicates the maximum likelihood SNR that caused the received iterate. The at least two factors may be alternating factors. The iterative root approximation technique using modified Newton-Raphson equations renders minima into repulsive fixed points and maxima into attractive fixed points.
The running weighted average may use a reciprocal of a probability of a data pair as weighting values in the running weighted average and the data pair may comprise a received value of the iterate and the SNR most likely to have caused the received value. A first derivative and a second derivative of the received value PDF are calculated for use in the iterative root approximation optimization technique using closed form equations or using numerical differentiation. The instantaneous maximum likelihood SNR for each iterate may be determined using a Newton-Raphson iterative root approximation optimization technique or a modified Newton-Raphson root approximation. The instantaneous maximum likelihood SNR estimate may comprise: constructing a two dimensional probability model of a received probability density function; slicing the two dimensional model along an SNR axis; determining the maximum likelihood SNR for the current received value by using the two dimensional probability model in a Newton-Raphson iteration; and using a current average SNR value as feedback to the instantaneous maximum likelihood SNR estimator to determine if a local maximum instantaneous likelihood value close to the current average SNR value exists. The local maximum SNR is the SNR for the value of the signal, if a local maximum instantaneous likelihood value close to the current average SNR value exists. The global maximum value as the SNR may be saved for the value of the signal if a local maximum instantaneous likelihood value close to the current average SNR value does not exist, where the global maximum value is the maximum likelihood SNR value closest to the current average SNR estimate.
A method for displaying probability density function (PDF) dependency on signal-to-noise ratio (SNR) in a signal comprises, for each iterate value of the signal: displaying a two dimensional probability model of a received probability density function; displaying a maximum likelihood SNR for a current received value on the two dimensional model sliced along an SNR axis; displaying a local instantaneous maximum likelihood value as the SNR if a local maximum likelihood value close to the current average SNR exists; and displaying a global maximum value as the SNR if a local instantaneous maximum value close to the current average SNR does not exist.
The computer instructions in the form of computer executable software code for implementing the above methods may be stored on computer-readable media.